Abstract: Many biophysical processes can be accurately modeled as a system stochastically exploring a discrete and connected network of possible states. Probability distributions over this space are not only subject to the system's intrinsic noisy dynamics, but may also be influenced by externally imposed perturbations. While results such as the Fluctuation-Dissipation Theorem allow for a precise understanding of how such perturbations may affect observable quantities on the system, these only properly function at equilibrium. Here, we explore the case of perturbations on nonequilibrium stochastic systems and derive a new response formula based on the Matrix-Tree Theorem approach. In particular, we derive the tightest possible linear bounds to sensitivity in arbitrary observables based on only the topology of the state network. These bounds stem from achetypical primitive models we call "uniquely constructable sets" that dictate the system properties under extreme conditions. As an exploratory example, we investigate a model of a macromolecule with three ligand binding sites to showcase how the uniquely constructable sets can be used to find all possible variations that are capable of maximizing the sensitivity of the number of bound sites relative to the external ligand concentration.

Contact: AIM Seminar Organizers